Abstract
The canonical decomposition of a Lorentz algebra element into a sum of orthogonal simple (decomposable) Lorentz bivectors is defined and discussed. This decomposition on the Lie algebra level leads to a natural decomposition of a proper orthochronous Lorentz transformation into a product of commuting Lorentz transformations, each of which is the exponential of a simple bivector. While this later result is known, we present novel formulas that are independent of the form of the Lorentz metric chosen. As an application of our methods, we obtain an alternative method of deriving the formulas for the exponential and logarithm for Lorentz transformations.
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Hanson, J. Orthogonal decomposition of Lorentz transformations. Gen Relativ Gravit 45, 599–612 (2013). https://doi.org/10.1007/s10714-012-1489-2
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DOI: https://doi.org/10.1007/s10714-012-1489-2